An interior ballistic optimization design method for an ultra-high-speed fragment launching device

Abstract

The application discloses an optimization design method of interior ballistic charge parameters of an ultrahigh-speed fragment launching device. The method adopts a multi-objective simulated annealing algorithm, combines an ultrahigh-speed fragment launching device interior ballistic calculation program and a Runge-Kutta equation solution program, and solves the problem that in the design of an ultrahigh-speed fragment charge, the ultrahigh-speed fragment launching device charge design meeting certain test target requirements cannot be quickly and accurately found, and is suitable for solving the optimization target requirements of various ultrahigh-speed fragment tests.

Description

Technical Field

[0001] This invention belongs to the field of internal ballistic optimization calculation and design, specifically, it is a method for optimizing the internal ballistic charge parameters of an ultra-high-speed fragmentation launching device. Background Technology

[0002] Hypervelocity fragmentation launch systems are primarily used to provide pre-formed fragments with relatively regular shapes, moving at high speeds to simulate high-speed shrapnel generated by ammunition explosions. In the field of ammunition safety, they are used to study the possible responses and damage modes of ammunition subjected to direct impact from high-speed shrapnel in battlefield environments. Based on the test results, ammunition safety is evaluated, and safety protection measures should be determined for actual storage and use. Furthermore, hypervelocity fragmentation launch systems are a much-needed testing platform for ammunition safety testing. Currently, there are no detailed research papers or materials on fragmentation launch systems, both domestically and internationally. Internal ballistic simulation of conventional ammunition calculates the corresponding internal ballistic results for a specific caliber and propellant. However, in ammunition fragment impact safety testing, fragment velocity and mass are crucial evaluation indicators. To meet testing requirements, continuous adjustments to the propellant parameters are needed to find internal ballistic propellant parameters that satisfy the current fragmentation test velocity requirements.

[0003] Therefore, accurately and quickly finding the internal ballistic charge parameters of the hypersonic fragment launcher that meet the experimental requirements and ensure the normal operation of the experiment is of paramount importance. Traditional hypersonic fragment testing still relies on manual adjustment of internal ballistic parameters to achieve the desired fragment velocity. This method consumes a great deal of human and computational resources and cannot simultaneously consider multiple optimization objectives. Therefore, how to quickly design the internal ballistic charge of the hypersonic fragment launcher that meets the experimental requirements, thereby reducing the human resource consumption during the testing process, is also a current research focus. Summary of the Invention

[0004] This invention primarily addresses the challenge of achieving ultra-high-speed propellant design at 2400 m / s when the initial fragment velocity is below the maximum average chamber pressure, making accurate and high-quality propellant loading impossible. Therefore, this invention provides a method for optimizing the internal ballistic propellant loading design in an ultra-high-speed fragmentation launch system.

[0005] To solve the above problems, the present invention adopts the following technical solution:

[0006] A method for optimizing the internal trajectory of a high-speed fragmentation launcher includes the following steps:

[0007] Step 1: For the hypersonic fragment launcher to be optimized, determine the target parameters for optimization design: hypersonic fragment velocity greater than 2400 m / s and maximum average pressure inside the barrel not exceeding 410 MPa; determine the variable range of propellant design parameters: propellant force f ranges from 900 kJ / kg to 950 kJ / kg, 1 / 2 arc thickness e1 ranges from 0.2 mm to 0.4 mm, aperture d0 ranges from 0.2 mm to 0.4 mm, burning rate coefficient u1 ranges from 1.6e-8 to 1.8e-8, and burning number index n ranges from 0.82 to 0.85. Randomly select a value from these parameter ranges as the initial value for the hypersonic fragment internal ballistic optimization calculation.

[0008] Step 2: Based on the initial parameters of the hypersonic fragment propellant charge design selected in Step 1, build an internal ballistic calculation model for the 30mm hypersonic fragment launcher.

[0009] Step 3: For the ballistic calculation model of the 30mm hypersonic fragment launcher established in Step 2, the Runge-Kutta method is used to solve it and obtain the specific values ​​of the ballistic characteristic parameters of the 30mm hypersonic fragment launcher. The results with fragment velocity above 1500m / s and maximum average pressure below 410MPa are used as the initial results. If the results do not meet the requirements, Step 1 is repeated.

[0010] Step 4: A new multi-objective acceptance criterion is adopted. Based on the original acceptance criterion, a probabilistic acceptance of suboptimal solutions is added under the condition of satisfying fragment velocity and maximum chamber pressure. The maximum number of Pareto solutions is set to 10-20. When setting the global optimal solution set, the first solution in the Pareto solution set is taken as the global optimal solution. After every 50-100 optimization calculations, the solutions in the Pareto solution set are compared with the solutions in the global optimal solution set, and the global optimal solution is updated accordingly. This method builds an improved multi-objective simulated annealing algorithm. The computational solution model jointly built in Steps 2 and 3 is used as the objective function of the improved multi-objective simulated annealing algorithm and embedded into the improved multi-objective simulated annealing algorithm model established in Step 4. Simultaneously, the initial results obtained in Step 3 are used as the initial random solution of the improved multi-objective simulated annealing algorithm model, thus obtaining the internal ballistic optimization model of the ultra-high-speed fragmentation launching device.

[0011] Step 5: For the optimization of the internal ballistics calculation of ultra-high-speed fragments, the target fragment velocity is greater than 2400m / s and the maximum pressure inside the chamber is less than 410MPa. The internal ballistics optimization model of the 30mm ultra-high-speed fragment launching device is used to perform optimization calculations to obtain the internal ballistics charge design parameters that meet the requirements of such ultra-high-speed fragment launching velocity and chamber pressure.

[0012] Preferably, the specific equations of the established internal ballistic calculation model are as follows:

[0013] Gunpowder burning rate equation:

[0014]

[0015]

[0016] Where Z is the relative combustion thickness, Z k Let ψ be the gunpowder combustion split point, ψ be the percentage of gunpowder combustion, and χ, λ, μ, χ s , λ s Here, u1 is the burning rate coefficient, e1 is half the arc thickness, p is the barrel pressure, and n is the burning rate index.

[0017] Equation of motion of the projectile:

[0018]

[0019] Where S is the cross-sectional area of ​​the launching device, φ is the secondary work coefficient, v is the fragment velocity, m is the fragment mass, and l is the fragment stroke.

[0020] Calculate the energy balance equation:

[0021]

[0022] Where l0 is the length of the gun chamber, f is the propellant force, ω is the charge amount, Δ is the charge density, and ρ is the charge density. p Let θ be the density of the gunpowder gas, θ be the specific heat coefficient, and α be the excess volume.

[0023] Compared with traditional propellant design technology, the beneficial effects that this invention can achieve are as follows:

[0024] It solves the problem that traditional internal ballistic optimization design cannot achieve a high speed of 2400m / s for fragment initial velocity while keeping the maximum average chamber pressure below the maximum limit, thus reducing the consumption of human and computing resources. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the trajectory calculation and operation within the ultra-high-speed launch device.

[0026] Figure 2 This is a schematic diagram of the Runge-Kutta method program.

[0027] Figure 3 The program execution diagram shows the multi-objective simulated annealing algorithm.

[0028] Figure 4 This relates the number of search attempts by the algorithm to the fragmentation rate.

[0029] Figure 5To optimize the internal ballistic VT diagram of ultra-high-speed fragments of explosive charges.

[0030] Figure 6 To optimize the internal ballistic trajectory plot of ultra-high-speed fragments of the explosive charge. Detailed Implementation

[0031] The invention will now be further described with reference to the accompanying drawings.

[0032] This invention discloses a ballistic optimization design method for an ultra-high-speed fragmentation launching device, specifically comprising the following steps:

[0033] (1) For the ultra-high-speed fragmentation device to be optimized, determine the target parameters required for the optimization design.

[0034] The structural parameters of the hypersonic launcher involved in the calculations and the required fragmentation velocities and maximum average chamber pressures were determined. Based on these specific parameters, an optimized design was performed on a 30mm hypersonic fragment launcher. Using a 300g propellant charge, the propellant parameters were optimized, including propellant force f, propellant particle arc thickness e1, propellant particle inner diameter d0, burning rate coefficient u1, and burning rate exponent n. The optimization objective was to achieve a muzzle velocity greater than 2400m / s and a lower average maximum pressure, while ensuring the average maximum pressure did not exceed 410MPa. This was achieved using a multi-objective simulated annealing algorithm.

[0035] The variation range of variable charge design parameters is specified, and the variable range of propellant design parameters is determined. The propellant force f ranges from 900 kJ / kg to 950 kJ / kg, the 1 / 2 arc thickness e1 ranges from 0.2 mm to 0.4 mm, the aperture d0 ranges from 0.2 mm to 0.4 mm, the burning rate coefficient u1 ranges from 1.6e-8 to 1.8e-8, and the burning number index n ranges from 0.82 to 0.85, to ensure the feasibility of the optimized calculation results of the charge parameters. A value is randomly selected from this parameter range as the initial value for the optimized calculation of the internal ballistics of the hypervelocity fragment.

[0036] (2) Based on the initial parameters of the ultra-high speed fragment propellant charge design selected in step 1, a ballistic calculation model of the 30mm ultra-high speed fragment launching device was built.

[0037] in accordance with Figure 1 Based on the calculation flowchart and the following internal ballistic calculation equations, a relevant calculation model is built.

[0038] Gunpowder burning rate equation:

[0039]

[0040] Where Z is the relative combustion thickness, Z kLet ψ be the gunpowder combustion split point, ψ be the percentage of gunpowder combustion, and χ, λ, μ, χ s , λ s Here, u1 is the burning rate coefficient, e1 is half the arc thickness, p is the barrel pressure, and n is the burning rate index.

[0041] Equation of motion of the projectile:

[0042]

[0043] Where S is the cross-sectional area of ​​the launching device, φ is the secondary work coefficient, v is the fragment velocity, m is the fragment mass, and l is the fragment stroke.

[0044] Calculate the energy balance equation:

[0045]

[0046] Where l0 is the length of the gun chamber, f is the propellant force, ω is the charge amount, Δ is the charge density, and ρ is the charge density. p Let θ be the density of the gunpowder gas, θ be the specific heat coefficient, and α be the excess volume.

[0047] The initial values ​​selected in step 1 are then substituted into the ballistic calculation model within the hypersonic launch device to prepare for the initial result calculation.

[0048] (3) The internal ballistic calculation model of the 30mm ultra-high speed fragment launching device established in step 2 is solved by the Runge-Kutta method to obtain the specific values ​​of its optimization target, namely fragment velocity and maximum average pressure.

[0049] according to Figure 2 The Runge-Kutta method calculation flowchart is shown. A program is built to solve the ballistic equations of the ultra-high-speed fragment launcher to obtain the specific values ​​of the ballistic characteristic parameters of the 30mm ultra-high-speed fragment launcher. The results with fragment velocities above 1500m / s and maximum average pressure below 410MPa are used as the initial results. Results that do not meet the requirements are repeated in step 1.

[0050] (4) In order to record the initial results calculated in step 3 and search for a better charge parameter structure, an improved multi-objective simulated annealing algorithm calculation model was built. The internal ballistic calculation model of the 30mm ultra-high speed fragment launcher and the relevant calculation model written by Runge-Kutta method were used as the objective function in the improved multi-objective simulated annealing algorithm model, so as to obtain the internal ballistic optimization model of the ultra-high speed launcher.

[0051] like Figure 3As shown in the figure, the present invention adopts an improved SMOSA algorithm and a new multi-objective acceptance criterion. That is, on the basis of the original acceptance criterion, a method of probabilistically accepting suboptimal solutions under multi-objective conditions (fragment velocity and maximum chamber pressure) is added, and the maximum number of Pareto solution sets is set to 10 (which can fully accept all solutions that meet the multi-objective requirements). When setting the global optimal solution set, the first solution in the Pareto solution set is used as the global optimal solution, and after every 50 optimization calculations, the solutions in the Pareto solution set are compared with the solutions in the global optimal solution set, and the global optimal solution is updated. The specific steps are as follows:

[0052] Step 1: Randomly initialize the solution set x of parameters, calculate all its objective functions, and add their objective function values to the Pareto solution set (non-dominated solution set).

[0053] Step 2: Given a random perturbation, let it generate a neighborhood solution set y of the x solution set, and substitute the y solution set into the objective function to calculate all its objective function values.

[0054] Step 3: Compare the objective function values of the newly generated neighborhood solution with the objective function values in the Pareto solution set. At this time, there are three situations. First, if the newly generated neighborhood solution is better than any solution in the Pareto solution set, then update the y solution set into the Pareto solution set, replace the x solution set with the y solution set, and go to Step 4. Second, if the newly generated neighborhood solution does not enter the Pareto solution set, then accept the new solution according to the following probability:

[0055]

[0056] And generate a random number t in the range (0, 1). If p > t, then replace the x solution set with the y solution set and go to Step 4.

[0057] Third, if p < t, it means that the new solution is not accepted, then keep the current solution and enter Step 4.

[0058] Step 4: Every certain number of generations k, randomly select a solution from the Pareto set as the initial solution and re-search.

[0059] Step 5: Cool down once every certain number of generations.

[0060] Step 6: Repeat Steps 2 to 5 until the temperature drops to the lowest temperature.

[0061] Taking Steps 2 and 3 as the objective functions and combining them in the multi-objective simulated annealing algorithm, the interior ballistic optimization model of the hypervelocity launch device is obtained.

[0062] The random solutions generated by the multi-objective simulated annealing algorithm are set as the input data for the ballistic calculation model inside the hypersonic launcher. The fragment velocity and maximum average pressure calculated by the model are used as objective function values ​​and substituted into the multi-objective simulated annealing algorithm for optimization calculation to obtain the ballistic optimization model inside the hypersonic launcher.

[0063] (5) For the optimization of the internal ballistics calculation of ultra-high speed fragments, the target fragment velocity is greater than 2400 m / s and the maximum pressure inside the chamber is less than 410 MPa. The internal ballistics optimization model of the 30mm ultra-high speed fragment launching device is used to perform optimization calculations and obtain the internal ballistics charge design parameters that meet the requirements of ultra-high speed fragment launching velocity and chamber pressure.

[0064] The basic parameters of the optimization model, such as the number of cycles, are set, and then the internal ballistics of the ultra-high-speed fragmentation launcher are optimized to obtain the optimal propellant design. The search process is as follows: Figure 4 As shown, the optimal solution and its charge configuration structure are shown in the table below.

[0065]

[0066]

[0067] Figure 5 , Figure 6 The calculated internal ballistic characteristic parameter curves of the ultra-high-speed internal ballistic optimized charge are used to calculate the internal ballistic characteristic parameters.

[0068] The above results show that, based on a 300g propellant charge, the optimal solution is the one that comprehensively considers both the maximum initial velocity and the average maximum chamber pressure.

[0069] This invention first addresses the limitation of traditional internal ballistic optimization design, which fails to achieve a fragment initial velocity of 2400 m / s under the condition that the maximum chamber pressure does not exceed the maximum barrel pressure of 410 MPa. Furthermore, it simultaneously considers minimizing the maximum average chamber pressure while achieving ultra-high-speed fragmentation. This two-pronged approach to internal ballistic optimization design overcomes the drawback of traditional optimization designs that only calculate the initial velocity.

[0070] Traditional internal ballistic optimization design achieves a suitable internal ballistic design by selecting standard propellant. This is one reason why traditional optimization designs cannot achieve ultra-high speeds for fragment velocities while maintaining maximum average chamber pressure. The ultra-high speed fragment internal ballistic optimization design employed in this invention offers greater flexibility in propellant parameter selection, not being limited to standard propellants. Therefore, the propellant charge design can be more flexible, leading to better design solutions and enabling fragment velocities to reach ultra-high speed levels.

[0071] Furthermore, traditional charge design largely relies on manual adjustments and calculations of relevant parameters, consuming significant human resources. The parameters chosen are also heavily influenced by subjective human factors and fail to comprehensively consider the results of all parameters. This invention performs a global search, introduces a method that accepts deteriorating solutions with a certain probability, and incorporates a optimal solution set system. During the optimization calculation process, it randomly re-searches, avoiding getting trapped in local optima and missing the optimal solution set. This invention saves human computational resources and obtains the optimal charge design scheme under the condition of comprehensively considering the calculation results of all parameters.

Claims

1. A ballistic optimization design method for an ultra-high-speed fragmentation launching device, characterized in that, It includes the following steps: Step 1: For the hypervelocity fragment launching device to be optimized and calculated, determine the target requirement parameters to be optimized and designed, determine the variable range of the initial parameters of the hypervelocity fragment propellant charge design, and randomly select a value within these parameter ranges as the initial value for the hypervelocity fragment interior ballistics optimization calculation; Step 2: Based on the initial value of the hypervelocity fragment propellant charge design selected in Step 1, build an interior ballistics calculation model for the 30mm hypervelocity fragment launching device; Step 3: For the interior ballistics calculation model of the 30mm hypervelocity fragment launching device established in Step 2, use the Runge-Kutta method for solution to obtain the specific values of the interior ballistics characteristic parameters of the 30mm hypervelocity fragment launching device. Take the results with the fragment velocity above 1500 m / s and the maximum average pressure below 410 MPa as the initial results, and return the results that do not meet the requirements to Step 1; Step 4: Adopt a new multi-objective new acceptance criterion, that is, on the basis of the original acceptance criterion, add the probability of accepting the sub-optimal solution under the conditions of meeting the fragment velocity and the maximum chamber pressure, and set the maximum number of the Pareto solution set to 10 - 20; when setting the global optimal solution set, take the first solution of the Pareto solution set as the global optimal solution and compare the solutions in the Pareto solution set with the solutions in the global optimal solution set every 50 - 100 optimization calculations, and update the global optimal solution. Build an improved multi-objective simulated annealing algorithm; take the calculation and solution model jointly built in Step 2 and Step 3 as the objective function of the improved multi-objective simulated annealing algorithm and embed it into the improved multi-objective simulated annealing algorithm model established in Step 4. At the same time, take the initial result calculated in Step 3 as the initial random solution of the improved multi-objective simulated annealing algorithm model to obtain the interior ballistics optimization model of the hypervelocity fragment launching device; The specific steps of the improved multi-objective simulated annealing algorithm are as follows: Step 1: Randomly generate an initial solution set x of parameters, calculate all its objective functions, and add their objective function values to the Pareto solution set; Step 2: Given a random perturbation, let it generate a neighborhood solution set y of the x solution set, and substitute the y solution set into the objective function to calculate all its objective function values; Step 3; Compare the objective function values of the newly generated neighborhood solution with the objective function values in the Pareto solution set. At this time, there are 3 situations. First, the newly generated neighborhood solution is better than any solution in the Pareto solution set. At this time, update the y solution set into the Pareto solution set, replace the x solution set with the y solution set, and go to Step 4; Second, if the newly generated neighborhood solution does not enter the Pareto solution set, then accept the new solution according to the following probability: And generate a random number t in the range of (0, 1). If p > t, then replace the x solution set with the y solution set and go to Step 4; Third, if p < t, it means that the new solution is not accepted, then keep the current solution and enter Step 4; Step 4: Every certain number of generations k, randomly select a solution from the Pareto set as the initial solution and search again; Step 5: Cool down once every certain number of algebras; Step 6: Repeat Step 2 to Step 5 until the temperature drops to the lowest possible level; Step 5: To optimize the fragment velocity and maximum average pressure inside the chamber of the ultra-high-speed fragment launcher, the internal ballistic optimization model of the 30mm ultra-high-speed fragment launcher was built to perform optimization calculations and obtain the internal ballistic charge design parameters that meet the requirements of ultra-high-speed fragment launch velocity and chamber pressure.

2. The ballistic optimization design method for the ultra-high-speed fragment launching device according to claim 1, characterized in that, The target parameters mentioned in step 1 include: ultra-high-speed fragment velocity greater than 2400 m / s, maximum average pressure inside the barrel of the ultra-high-speed fragment launching device not exceeding 410 MPa; the variable range of propellant design parameters is: propellant force f ranging from 900 kJ / kg to 950 kJ / kg, 1 / 2 arc thickness e1 ranging from 0.2 mm to 0.4 mm, aperture d0 ranging from 0.2 mm to 0.4 mm, burning rate coefficient u1 ranging from 1.6e-8 to 1.8e-8, and burning index n ranging from 0.82 to 0.

85.

3. The ballistic optimization design method for the ultra-high-speed fragment launching device according to claim 1, characterized in that, The specific equations for the ballistic calculation model of the ultra-high-speed fragmentation launching device established in step 2 are as follows: Gunpowder burning rate equation: Where Z is the relative combustion thickness, Z k Let ψ be the gunpowder combustion split point, ψ be the percentage of gunpowder combustion, and χ, λ, μ, χ s , λ s Here, u1 is the burning rate coefficient, e1 is 1 / 2 arc thickness, p is the internal pressure, and n is the burning rate index. Equation of motion of the projectile: Where S is the cross-sectional area of ​​the launching device, φ is the secondary work coefficient, v is the fragment velocity, m is the fragment mass, and l is the fragment stroke. Calculate the energy balance equation: Where l0 is the length of the gun chamber, f is the propellant force, ω is the charge amount, Δ is the charge density, and ρ is the charge density. p Let θ be the density of the gunpowder gas, θ be the specific heat coefficient, and α be the excess volume.

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